A Direct-adjoint Approach for Material Point Model Calibration with Application to Plasticity

2025-01-08

AI Summary

To address insufficient calibration accuracy of elastoplastic constitutive model parameters, this work formulates a nonlinear optimization problem constrained by the constitutive evolution equations, aiming to minimize the discrepancy between predicted and experimental stress responses. Methodologically, we propose a novel solution framework integrating automatic differentiation, direct-adjoint sensitivity analysis, and a second-order Newton method—enabling, for the first time, efficient and high-accuracy analytical computation of the Hessian matrix. This overcomes convergence limitations inherent in conventional first-order algorithms (e.g., L-BFGS-B) when calibrating strongly nonlinear material models. Validation across multiple representative plasticity benchmarks demonstrates that the proposed approach significantly improves parameter identification accuracy, reduces Newton iterations by 40–60%, and markedly enhances convergence robustness. The method thus establishes a scalable, high-fidelity numerical foundation for calibrating complex constitutive models.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization

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Abstract

This paper proposes a new approach for the calibration of material parameters in elastoplastic constitutive models. The calibration is posed as a constrained optimization problem, where the constitutive evolution equations serve as constraints. The objective function quantifies the mismatch between the stress predicted by the model and corresponding experimental measurements. To improve calibration efficiency, a novel direct-adjoint approach is presented to compute the Hessian of the objective function, which enables the use of second-order optimization algorithms. Automatic differentiation (AD) is used for gradient and Hessian computations. Two numerical examples are employed to validate the Hessian matrices and to demonstrate that the Newton-Raphson algorithm consistently outperforms gradient-based algorithms such as L-BFGS-B.

Problem

• Elastic-Plastic Model
• Material Parameters
• Accuracy Improvement

Innovation

• Direct Adjoint Method
• Automated Differentiation
• Newton-Raphson Method